Set Theory: Proving A-(BUC)=(A\cup B)-C

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Homework Help Overview

The discussion revolves around proving the set theory expression A - (B ∪ C) = (A ∪ B) - C. Participants are exploring the properties of set operations and simplifications involved in this proof.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss rewriting set subtractions for clarity and simplification. There are mentions of using Venn diagrams for testing equality and references to De Morgan's laws, although some suggest that other properties like distributivity and associativity may be more relevant.

Discussion Status

There is an ongoing exploration of different approaches to simplifying the right-hand side of the equation. Some participants have offered guidance on rewriting expressions and suggested focusing on specific set properties, but no consensus has been reached on a definitive method.

Contextual Notes

Participants express uncertainty about the format and requirements for presenting their proofs, indicating a need for clarity on how to structure their work.

Carmen12
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Homework Statement





[A-(BUC)]U[(A\cup B)-C]U[(A\cap C)-B]U[A\capB\capC];

The Attempt at a Solution



Sorry about the crappy formatting (btw).
Anyway, I'm trying to "prove" that this is is equal to A. So basically cancelling out the Bs and Cs? I'm not sure how to go about this. de morgan's laws? *sigh* I tested it with Venn Diagrams and it is equal to A.
 
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I would start be re-writing the subtractions a little more explicitly, as an example
A - B = A - A \cap B

this should lead to a few siplifications, and you should be able to apply de morgan's law more easily
 
Thank you so much! Some research on de morgan is in need!

I wish there was a calculator for this stuff. *sigh*

For the proof will just showing the calculations work? Or is there a particular way of writing it out I need?
 
just try and simplify the RHS as much as you can

and its not De Morgan's law you need, which deals with complements, its just distrbutivity & associtivity see the following

http://en.wikipedia.org/wiki/Algebra_of_sets
 

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